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11 papers · 1 filter
Coverings and liftings of generalized crossed modules
Gamze Aytekin Arici, Tunçar Şahan
In the theory of crossed modules, considering arbitrary self-actions instead of conjugation allows for the extension of the concept of crossed modules and thus the notion of genera…
Pentactions and action representability in the category of reduced groups with action
Tamar Datuashvili, Tunçar Şahan
A notion of pentaction of any object in the category of reduced groups with action is introduced. The operations are defined in the set $\mathsf{Pentact}(A…
Actions and semi-direct products in categories of groups with action
Tamar Datuashvili, Tunçar Şahan
Derived actions in the category of groups with action on itself are defined and described. This category plays a crucial role in the solution of Loday's two…
Groups up to congruence relation and from categorical groups to c-crossed modules
Tamar Datuashvili, Osman Mucuk, Tunçar Şahan
We introduce a notion of c-group, which is a group up to congruence relation and consider the corresponding category. Extensions, actions and crossed modules (c-crossed modules) ar…
Categories internal to crossed modules
Tunçar Şahan, Jihad Jamil Mohammed
In this study, internal categories in the category of the crossed modules are characterized and it has been shown that there is a natural equivalence between the category of the cr…
Crossed modules, double group-groupoids and crossed squares
Sedat Temel, Tunçar Şahan, Osman Mucuk
In this paper using split extensions of group-groupoids we obtain the notion of crossed modules over group-grouoids which are also called 2-groups and we prove a categorical equiva…